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Finite detection thresholds in bursty systems, like material deformation and earthquakes, create temporal correlations. This occurs by splitting large events into smaller sub-events, leading to observable clustering in activity.

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Area of Science:

  • Physics of complex systems
  • Materials science
  • Geophysics

Background:

  • Many natural and engineered systems exhibit bursty dynamics with broad event size distributions.
  • Temporal correlations, or clustering, are often observed in these bursty dynamics, indicated by power-law waiting times between events.

Purpose of the Study:

  • To explain the origin of temporal correlations in bursty dynamics.
  • To demonstrate how a finite detection threshold can induce these correlations.

Main Methods:

  • Analysis of crack-propagation experiments.
  • Numerical simulations of a nonequilibrium crack-line model.
  • Development of a general scaling description for thresholding-induced correlations.

Main Results:

  • Finite detection thresholds inherently lead to temporal correlations in bursty activity.
  • Thresholding causes large avalanche events to be separated into smaller sub-avalanches.
  • These subavalanche correlations are quantitatively described by the proposed scaling theory.

Conclusions:

  • The presence of a detection threshold is a fundamental mechanism generating temporal correlations in crackling noise.
  • Understanding thresholding effects is crucial for interpreting bursty dynamics in diverse scientific fields.